Data collection networks often sample data at a first location and then transmit the sampled data to another location for processing and analysis. In some data collection networks, data may be sampled randomly or irregularly as a function of time. In particular, a time interval between individual samples of a continuously time-varying signal may vary essentially randomly as a function of time.
Examples of such data collection networks include, but are not limited to, a wideband test system with random sampling and a time synchronized, low power network of sensors. A wideband test system with random sampling, when accompanied by accurate timestamping (e.g., time synchronization) of the samples, facilitates wideband signal characterization using average sample rates far below a conventional Nyquist sampling rate for the signal. In another wideband signal test situation, particular tests often require accurate data across limited spectral range (e.g., one-tone and two-tone tests of radio frequency devices). In such situations, randomized data sampling may minimize a total amount of data required for performing the tests. With respect to low-power networked sensors, a power consumption of each sensor is often directly related to a sample rate of the sensor. In many situations, reducing the data rate by employing randomized sampling facilitates low-power operation. In addition, constraints imposed by the network (e.g., network protocols and associated timing) often place practical restrictions on sampling intervals resulting in uneven or irregularly spaced samples. U.S. Pat. No. 6,735,539 B2 to Barford, incorporated herein by reference, teaches such a system using networked sensors with unevenly spaced samples having timestamps.
Median filtering is known by those of ordinary skill in the art as a non-linear digital filter technique suitable for continuously time-varying signals that is useful for purposes of removing noise in the data and signal smoothing. The median filter identifies an amplitude value wherein half of the time the data is above the median amplitude value and half of the time the data is below the median amplitude value.
A rank order filter is a more general filter based on the median filter concept wherein a percentage p between 0% and 100% may be selected. A rank order filter returns the amplitude value where p % of the data is below the returned amplitude value and (100−p) % of the data is equal to or above the returned amplitude value.
Publication entitled “Sorting Continuous-Time Signals and the Analog Median Filter”, authored by Paulo J. S. G. Ferreira published in the IEEE Signal Processing Letters, Vol. 7, No. 10, in October 2000, proposes a solution to median and rank order filtering in terms of distribution and rearrangement of data in a continuously time-varying function and analog filtering. While rank order analog filtering is a helpful discussion, there remains a practical solution for a digital median and rank order filter suitable for use on data sampled at random intervals of time.